# Skewing

**Skewing**, or **skew halving**, is an operation that can be performed on a regular polyhedron of Schläfli type {p,4}. It is represented with the symbol σ , and a polyhedron obtained from skewing will be self-Petrie.

It is equivalent to the composed operation π∘δ∘η∘π∘δ, although in some cases the intermediate stages of this process may be degenerate or impossible to realize, even though the end result can be realized in some cases (e.g. the skew muoctahedron).

## Definition[edit | edit source]

### Abstract polytopes[edit | edit source]

The skewing of a regular polyhedron with distinguished generators is the regular polyhedron generated by the distinguished generators:

## Related operations[edit | edit source]

### Generalized skewing[edit | edit source]

There also exists a **generalized skewing operation** defined on polyhedra with a -gonal vertex figure. It can be defined in terms of the generalized halving operation as .

### ς [edit | edit source]

The related opration **ς ** is skewing applied to the dual.^{[1]} It can be seen as a shorthand for δ σ .

## References[edit | edit source]

## Bibliography[edit | edit source]

- McMullen, Peter (2009), "Regular apeirotopes of dimension and rank 4",
*Discrete computational geometry*

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